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We study the problem of testing discrete distributions with a focus on the high probability regime. Specifically, given samples from one or more discrete distributions, a property $\mathcal{P}$, and parameters $0< \epsilon, \delta <1$, we…

Data Structures and Algorithms · Computer Science 2020-09-15 Ilias Diakonikolas , Themis Gouleakis , Daniel M. Kane , John Peebles , Eric Price

We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…

Statistics Theory · Mathematics 2021-06-01 Liyan Xie , Rui Gao , Yao Xie

We demonstrate one-sided device-independent self-testing of any pure entangled two-qubit state based on a fine-grained steering inequality. The maximum violation of a fine-grained steering inequality can be used to witness certain steerable…

Quantum Physics · Physics 2020-05-06 Zhihao Bian , A. S. Majumdar , C. Jebaratnam , Kunkun Wang , Lei Xiao , Xiang Zhan , Yongsheng Zhang , Peng Xue

Unsharp quantum measurements provide a resource in scenarios where one faces the trade-off between information gain and disturbance. In this work we introduce a prepare-transform-measure scenario in which two-outcome unsharp measurements…

Quantum Physics · Physics 2020-07-07 Nikolai Miklin , Jakub J. Borkała , Marcin Pawłowski

We establish a quantitative relation between Hardy's paradox and the breaking of uncertainty principle in the sense of measurement-disturbance relations in the conditional measurement of non-commuting operators. The analysis of the…

Quantum Physics · Physics 2015-06-23 Kazuo Fujikawa , C. H. Oh , Sixia Yu

In quantum cryptography, device-independent (DI) protocols can be certified secure without requiring assumptions about the inner workings of the devices used to perform the protocol. In order to display nonlocality, which is an essential…

Quantum Physics · Physics 2018-08-23 Cédric Bamps , Serge Massar , Stefano Pironio

Device-independent quantum key distribution allows for proving the security of a shared cryptographic key between two distant parties with potentially untrusted devices. The security proof is based on the measurement outcome statistics…

Quantum Physics · Physics 2023-10-23 Máté Farkas

In this paper, we analyze several critical issues in semi-device independent quantum information processing protocol. In practical experimental realization randomness generation in that scenario is possible only if the efficiency of the…

Quantum Physics · Physics 2015-06-23 Hong-Wei Li , Zhen-Qiang Yin , Marcin Pawlowski , Guang-Can Guo , Zheng-Fu Han

Hardy's argument constitutes an elegant proof of quantum nonlocality. In this work, we report an exotic application of Hardy's nonlocal correlations in two-party communication setup. We come up with a task, wherein a positive payoff can be…

Quantum correlations and non-projective measurements underlie a plethora of information-theoretic tasks, otherwise impossible in the classical world. Existing schemes to certify such non-classical resources in a device-independent manner…

It is well-known that observing nonlocal correlations allows us to draw conclusions about the quantum systems under consideration. In some cases this yields a characterisation which is essentially complete, a phenomenon known as…

Quantum Physics · Physics 2020-04-02 Tim Coopmans , Jędrzej Kaniewski , Christian Schaffner

We generalize Hardy's proof of nonlocality to the case of bipartite mixed statistical operators, and we exhibit a necessary condition which has to be satisfied by any given mixed state $\sigma$ in order that a local and realistic hidden…

Quantum Physics · Physics 2009-11-13 GianCarlo Ghirardi , Luca Marinatto

A recent sequence of works, initially motivated by the study of the nonlocal properties of entanglement, demonstrate that a source of information-theoretically certified randomness can be constructed based only on two simple assumptions:…

Quantum Physics · Physics 2013-06-25 Matthew Coudron , Thomas Vidick , Henry Yuen

By applying Hardy's argument, we demonstrate the violation of local realism in a gedanken experiment using independent and separated particle sources.

Quantum Physics · Physics 2009-11-07 Xu-Bo Zou , Hai-Woong Lee , Jaewan Kim , Jae-Weon Lee , Eok Kyun Lee

Quantum nonlocality offers a secure way to produce random numbers: their unpredictability is intrinsic and can be certified just by observing the statistic of the measurement outcomes, without assumptions on how they are produced. To do…

The question of certifying quantum nonlocality under a relaxation of the assumptions in the Bell theorem has gained traction, with potential for device-independent applications under weak seeds and cross-talk. Recently, it was shown that…

Quantum Physics · Physics 2025-12-23 Ravishankar Ramanathan , Yuan Liu

The randomness from a quantum random number generator (QRNG) relies on the accurate characterization of its devices. However, device imperfections and inaccurate characterizations can result in wrong entropy estimation and bias in practice,…

Quantum Physics · Physics 2016-12-30 You-Qi Nie , Jian-Yu Guan , Hongyi Zhou , Qiang Zhang , Xiongfeng Ma , Jun Zhang , Jian-Wei Pan

Bell nonlocality provides a device-independent (DI) way to certify quantum randomness, based on which true random numbers can be extracted from the observed correlations without detail characterizations on devices for quantum state…

Quantum Physics · Physics 2026-01-27 Shuai Zhao , Rong Wang , Qi Zhao

Reliable randomness is a core ingredient in algorithms and applications ranging from numerical simulations to statistical sampling and cryptography. The outcomes of measurements on entangled quantum states can violate Bell inequalities,…

From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A…

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